The range of a Lévy process
It is shown that all Lévy processes on the line whose paths are of bounded variation have a closed range over any finite time interval that is nowhere dense except for those processes having positive (negative) drift with Lévy measure finite on (0,\(\infty)\) (finite on (- \(\infty,0))\). The proof is relied upon M. T. Barlow's 0-1 law and the fact that any cadlag process which fails to hit points has nowhere dense closed range over any finite time interval.
scientific article; zbMATH DE number 4192773